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Paper Citation Record · LEDGER

Singularities of massless scattering and cluster algebras

As of 8 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 3 inbound Pith citation observations for arXiv:2507.01015.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.01015 v1

Coverage vector

measured 58 of 58 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:09:07.810683Z

measured 61 of 61 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T23:22:48.010474Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-01T17:05:50.640634Z

Reference resolution

58 of 58 outbound references displayed

  • verified exact15
  • verified fuzzy22
  • unresolved21
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bf60e181-5f7c-4db6-b2cb-d5542633da83 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 1

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Observation 6a2c37d3-9f90-4886-923f-8b7cbaa778f8 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 2

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Observation 4f97bfc5-48f5-41fd-a3ec-f9a253b82352 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 3

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Observation 83f13ed8-9c4f-4d7e-bf21-f8a5a3b8a4f6 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 4

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Observation a0b34686-cb8d-4267-85e1-d40bca7ba5d8 · outbound

This paper cites Written in terms of spinor brackets, letters V6 to V21 from the non-planar two-loop five-point alphabet are quadratic.

Singularities of massless scattering and cluster algebras Written in terms of spinor brackets, letters V6 to V21 from the non-planar two-loop five-point alphabet are quadratic

Reference 5

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Observation 3323056d-dc0f-43c9-a959-2db3eee2c991 · outbound

This paper cites Each quadratic letter is of the form Qi,j;k,l;m = si,j − sk,l (37) for {i, j, k, l, m} = {1, 2, 3, 4, 5}.

Singularities of massless scattering and cluster algebras Each quadratic letter is of the form Qi,j;k,l;m = si,j − sk,l (37) for {i, j, k, l, m} = {1, 2, 3, 4, 5}

Reference 6

Resolution
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Observation bb50382a-ec9d-4a47-a632-8f44576dd50e · outbound

This paper cites These are the pairs of quadratics which appear separated by one slot in presently computed two-loop planar data, e.g.

Singularities of massless scattering and cluster algebras These are the pairs of quadratics which appear separated by one slot in presently computed two-loop planar data, e.g

Reference 7

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Observation 9fa1671c-9321-4083-87e8-8525103c29e0 · outbound

This paper cites These appear separated by one slot in non-planar data, with a unique combi- nation sitting between.

Singularities of massless scattering and cluster algebras These appear separated by one slot in non-planar data, with a unique combi- nation sitting between

Reference 8

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Observation 5ee90f54-e25b-45ba-9a74-ea167a672dd1 · outbound

This paper cites Cluster algebras i: Foundations, 2001.

Singularities of massless scattering and cluster algebras Cluster algebras i: Foundations, 2001

Reference 9

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Observation 02a7250b-3850-4025-9099-4004de0e4d7d · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 10

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Observation 162d03f3-6a15-4bb0-9df5-bb9aca2d82fe · outbound

This paper cites Five of the algebraic letters are these naked discriminants.

Singularities of massless scattering and cluster algebras Five of the algebraic letters are these naked discriminants

Reference 11

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation c7c3f2ee-b7f4-468e-85af-0f4f87ccbd88 · outbound

This paper cites An example of an origin cluster is shown in Figure 5.

Singularities of massless scattering and cluster algebras An example of an origin cluster is shown in Figure 5

Reference 12

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 23505040-1b54-456c-8fbf-954106c8726e · outbound

This paper cites (18) The map in the other direction, from four-index Pl¨ ucker coordinates to square and angle brackets, is sim- ilarly straightforward.

Singularities of massless scattering and cluster algebras (18) The map in the other direction, from four-index Pl¨ ucker coordinates to square and angle brackets, is sim- ilarly straightforward

Reference 13

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Observation 518ad081-5afb-4f62-9964-f556c509b96c · outbound

This paper cites The only difference is that there are now only 16 different origin clusters, each of which asymptotes to the same ray.

Singularities of massless scattering and cluster algebras The only difference is that there are now only 16 different origin clusters, each of which asymptotes to the same ray

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:09:15.764170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 1aab7b11-66c4-41a9-81f1-f419c0b6e2c6 · outbound

This paper cites This class seems to have a realisation in the flag, specifi- cally using the momentum twistor embedding.

Singularities of massless scattering and cluster algebras This class seems to have a realisation in the flag, specifi- cally using the momentum twistor embedding

Reference 15

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Observation 8ef6d288-7639-4571-8e15-7b080d3d1a0e · outbound

This paper cites Since W61 is one of the letters which we fail to reproduce in either embedding of the kinematics, we cannot hope to realise this inside F(2 , 4; 6).

Singularities of massless scattering and cluster algebras Since W61 is one of the letters which we fail to reproduce in either embedding of the kinematics, we cannot hope to realise this inside F(2 , 4; 6)

Reference 16

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Observation 5b51d159-5cc4-4270-870c-820e0e9518dc · outbound

This paper cites Express these in terms of the letters of the planar pentagon al- phabet.

Singularities of massless scattering and cluster algebras Express these in terms of the letters of the planar pentagon al- phabet

Reference 17

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Observation 241d6812-66b4-4b2e-88f0-2ca18e47b0ab · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 18

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Observation 41ffa800-0682-4658-b7aa-7d62ecc065f0 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 19

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Observation c5d9ecba-1f60-431b-bd79-abfcafecc11e · outbound

This paper cites Summer School in Total Positivity and Quantum Field Theory.

Singularities of massless scattering and cluster algebras Summer School in Total Positivity and Quantum Field Theory

Reference 20

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Observation 2f5a5ec8-cefb-4b6b-8503-04ba69f235cd · outbound

This paper cites Tropicalised braid automorphisms of grassmannian cluster algebras.

Singularities of massless scattering and cluster algebras Tropicalised braid automorphisms of grassmannian cluster algebras

Reference 21

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Observation fc2ce32d-3f40-4788-92b0-3d2c5e6c9bf2 · outbound

This paper cites Cluster structures on spinor helicity and momentum twistor varieties.

Singularities of massless scattering and cluster algebras Cluster structures on spinor helicity and momentum twistor varieties

Reference 22

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Observation 1195a7c7-fb71-46cf-bcc6-978da668e96d · outbound

This paper cites Symbol alphabets in qcd and flag cluster algebras, 2025.

Singularities of massless scattering and cluster algebras Symbol alphabets in qcd and flag cluster algebras, 2025

Reference 23

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 5b790e70-5d87-4ed5-bc88-c93b3be3ff58 · outbound

This paper cites Adjacency for scattering amplitudes from the Gr\"obner fan.

Singularities of massless scattering and cluster algebras Adjacency for scattering amplitudes from the Gr\"obner fan

Reference 24

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Observation df549e62-e5f3-4d01-90ef-76b56a596814 · outbound

This paper cites Dixon, James M.

Singularities of massless scattering and cluster algebras Dixon, James M

Reference 25

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source=pdf_text observed=2026-08-06T21:09:04.780038Z digest=sha256:b1d3382967799b7702db3f4b906b30e20f1627bcc5ecc60bebdb7b7a97dc0ad1

Observation 250e58b0-a016-4fd1-beed-8e64fa6df554 · outbound

This paper cites Dixon, James M.

Singularities of massless scattering and cluster algebras Dixon, James M

Reference 26

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doi, observed 2026-08-06T21:09:10.670438Z

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Observation c1235a11-0002-4e9a-8778-cf2364a7d184 · outbound

This paper cites Here we review the recovery of the symbol letters using both F(2 , n− 4; n) and F(2, 4; n) in the case n = 5.

Singularities of massless scattering and cluster algebras Here we review the recovery of the symbol letters using both F(2 , n− 4; n) and F(2, 4; n) in the case n = 5

Reference 27

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raw_fallback, observed 2026-08-06T21:09:18.160338Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 7976657d-75bf-4f9f-b5b6-7a8509174e11 · outbound

This paper cites Dixon, James M.

Singularities of massless scattering and cluster algebras Dixon, James M

Reference 28

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no resolver link, observed 2026-08-06T21:09:04.933435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T21:09:04.933435Z digest=sha256:9b617da854f5b38d5d91f41d74f8196b90b4e4df1e7d9622b792b720c1ab1128

Observation b7accffd-5a13-4288-a43b-cb3f5e70ea1a · outbound

This paper cites Cluster adjacency and the four-loop nmhv heptagon.

Singularities of massless scattering and cluster algebras Cluster adjacency and the four-loop nmhv heptagon

Reference 29

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verified exact
doi, observed 2026-08-06T21:09:10.443374Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation acfd001d-f1f6-496c-aa61-e82b4760ebd7 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 30

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Observation c1abed89-545a-48ec-aa7c-82b522adca23 · outbound

This paper cites Tropical grassmannians, clus- ter algebras and scattering amplitudes.

Singularities of massless scattering and cluster algebras Tropical grassmannians, clus- ter algebras and scattering amplitudes

Reference 31

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source=pdf_text observed=2026-08-06T21:09:07.394115Z digest=sha256:2f9ddb39d5131d7e581580d3738740bbce4c9409573fe127a8c17f53c55b7645

Observation 7d4fa3b3-efde-41af-ac68-f9a6c5365d5d · outbound

This paper cites Henn, and Georgios Pap- athanasiou.

Singularities of massless scattering and cluster algebras Henn, and Georgios Pap- athanasiou

Reference 32

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source=pdf_text observed=2026-08-06T21:09:05.233353Z digest=sha256:1a6f18952936dd4d4aeb60a5b644f56fadc6e3bd30a5df4c5e9002dc048b7a3c

Observation ed24367d-24e3-4b00-8e47-f40553f08d08 · outbound

This paper cites Dixon, ¨Omer G¨ urdo˘ gan, Yu-Ting Liu, An- drew J.

Singularities of massless scattering and cluster algebras Dixon, ¨Omer G¨ urdo˘ gan, Yu-Ting Liu, An- drew J

Reference 33

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doi, observed 2026-08-06T21:09:08.126779Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T21:09:07.591341Z digest=sha256:b1c19b4a9f9ac1e4dccc8842de4112da38ec15f60c7c54d329bf32a899ce2a4b

Observation c3c9f275-b6c4-48bb-9334-db6767bd81a8 · outbound

This paper cites The other rational letters missed in in the momentum twistor embedding are all permutations of this letter, and so the entire rational alphabet is recovered.

Singularities of massless scattering and cluster algebras The other rational letters missed in in the momentum twistor embedding are all permutations of this letter, and so the entire rational alphabet is recovered

Reference 34

Resolution
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raw_fallback, observed 2026-08-06T21:09:14.605281Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T21:09:04.278181Z digest=sha256:b4796adad9a197666bece4cbe9eaec65da4bed5db4579f51724c60fbc21dc96e

Observation f8f1d414-005b-4295-a3b8-deaa1ad4ff63 · outbound

This paper cites An Exceptional Cluster Algebra for Higgs plus Jet Production.

Singularities of massless scattering and cluster algebras An Exceptional Cluster Algebra for Higgs plus Jet Production

Reference 35

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Observation d942b962-314b-49d5-8585-07d2d76b0e70 · outbound

This paper cites For six particles, both partial flag varieties turn out to be F(2 , 4; 6).

Singularities of massless scattering and cluster algebras For six particles, both partial flag varieties turn out to be F(2 , 4; 6)

Reference 36

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Observation 4f5a159c-20da-44c6-806b-41f18c094542 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 37

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Observation e011764a-81cc-47af-85da-2a40a1035a91 · outbound

This paper cites Paulos, Marcus Spradlin, and Anastasia Volovich.

Singularities of massless scattering and cluster algebras Paulos, Marcus Spradlin, and Anastasia Volovich

Reference 38

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Observation 6d536432-cee9-478d-82d9-cc84c46a7f3f · outbound

This paper cites Dixon, James Drummond, Thomas Har- rington, Andrew J.

Singularities of massless scattering and cluster algebras Dixon, James Drummond, Thomas Har- rington, Andrew J

Reference 39

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Observation 377074aa-d798-4aef-a6eb-92050f0c6168 · outbound

This paper cites Algebraic singularities of scat- tering amplitudes from tropical geometry, 2021.

Singularities of massless scattering and cluster algebras Algebraic singularities of scat- tering amplitudes from tropical geometry, 2021

Reference 40

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Observation 28cd6672-dc81-442f-8827-18d2dd9a743d · outbound

This paper cites How tropical are seven- and eight-particle amplitudes? Journal of High Energy Physics , 2020(8), August 2020.

Singularities of massless scattering and cluster algebras How tropical are seven- and eight-particle amplitudes? Journal of High Energy Physics , 2020(8), August 2020

Reference 41

Resolution
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Observation aad3d6b6-e3a3-4ad5-b099-f193486c0867 · outbound

This paper cites Singulari- ties of eight- and nine-particle amplitudes from cluster algebras and tropical geometry.

Singularities of massless scattering and cluster algebras Singulari- ties of eight- and nine-particle amplitudes from cluster algebras and tropical geometry

Reference 42

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation ca005ceb-071b-45ad-819a-681f1a029765 · outbound

This paper cites Bourjaily, Andrew J.

Singularities of massless scattering and cluster algebras Bourjaily, Andrew J

Reference 43

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source=pdf_text observed=2026-08-06T21:09:05.997095Z digest=sha256:c15b1090f6f41abdbec31e2d12c784e542c76044a3c19ccd0038ce52f3030b87

Observation d110bba7-6dc7-4f8a-bbae-140850db8c2c · outbound

This paper cites Introduction to Cluster Algebras. Chapters 1-3.

Singularities of massless scattering and cluster algebras Introduction to Cluster Algebras. Chapters 1-3

Reference 44

Resolution
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source=pdf_text observed=2026-08-06T21:09:06.100645Z digest=sha256:aa11a8682b78507a20c008b0228102e0c8873335f3872f84658592486cb4c850

Observation d57d1c4d-9bb0-41db-a09d-719d8b1c818c · outbound

This paper cites Cluster Adjacency Properties of Scattering Ampli- tudes in N = 4 Supersymmetric Yang-Mills The- ory.

Singularities of massless scattering and cluster algebras Cluster Adjacency Properties of Scattering Ampli- tudes in N = 4 Supersymmetric Yang-Mills The- ory

Reference 45

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Observation ae9e57e5-548c-41d7-8bc1-d2c790d40f93 · outbound

This paper cites Partial flag varieties and preprojective algebras.

Singularities of massless scattering and cluster algebras Partial flag varieties and preprojective algebras

Reference 46

Resolution
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Observation bf6fbca0-b226-45bb-9392-152c56d988b1 · outbound

This paper cites Bootstrapping pentagon functions.

Singularities of massless scattering and cluster algebras Bootstrapping pentagon functions

Reference 48

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation e3ee30a7-3d0f-4c8a-a7d4-b533b37f36b1 · outbound

This paper cites Dixon, Enrico Herrmann, Ben Page, and Mao Zeng.

Singularities of massless scattering and cluster algebras Dixon, Enrico Herrmann, Ben Page, and Mao Zeng

Reference 49

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Observation 8f48a0f4-5037-40da-acea-776fc52305b3 · outbound

This paper cites Dixon, Enrico Herrmann, Ben Page, and Mao Zeng.

Singularities of massless scattering and cluster algebras Dixon, Enrico Herrmann, Ben Page, and Mao Zeng

Reference 50

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 5e495ec9-447c-49ba-946c-3cedce9b6e5d · outbound

This paper cites Pentagon Wilson loop with Lagrangian insertion at two loops in N = 4 super Yang-Mills theory, 2022.

Singularities of massless scattering and cluster algebras Pentagon Wilson loop with Lagrangian insertion at two loops in N = 4 super Yang-Mills theory, 2022

Reference 51

Resolution
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Observation 6421f0f4-376f-450e-9f81-49b5894b3b3c · outbound

This paper cites Abreu, J.

Singularities of massless scattering and cluster algebras Abreu, J

Reference 52

Resolution
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Observation 00731f55-84c2-4bc0-9dca-f2fc940801cc · outbound

This paper cites Complete function space for planar two-loop six-particle scattering amplitudes.

Singularities of massless scattering and cluster algebras Complete function space for planar two-loop six-particle scattering amplitudes

Reference 53

Resolution
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source=pdf_text observed=2026-08-06T21:09:07.255068Z digest=sha256:c595b7893e721c12f9c5080d7160dd08f5fb4432f5a51049daa2a550173e8f02

Observation 54469486-55a0-4f26-865b-9f5306824ebe · outbound

This paper cites Hexagonal Wilson loop with Lagrangian insertion at two loops in $\mathcal{N}=4$ super Yang-Mills theory.

Singularities of massless scattering and cluster algebras Hexagonal Wilson loop with Lagrangian insertion at two loops in $\mathcal{N}=4$ super Yang-Mills theory

Reference 55

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source=pdf_text observed=2026-08-06T21:09:07.505146Z digest=sha256:6d37ca929b22f33ebd043aed846fc376b9c440374b7f2c7e4d4156774ba6775c

Observation ad7c6f5b-ae1a-4d12-94d0-ee979327c5e5 · outbound

This paper cites The tropical totally positive Grassmannian.

Singularities of massless scattering and cluster algebras The tropical totally positive Grassmannian

Reference 57

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation c1df0678-6b41-46aa-a604-ce67545c3bfd · outbound

This paper cites An Analytic Computation of Three-Loop Five-Point Feynman Integrals.

Singularities of massless scattering and cluster algebras An Analytic Computation of Three-Loop Five-Point Feynman Integrals

Reference 58

Resolution
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source=pdf_text observed=2026-08-06T21:09:07.810683Z digest=sha256:811188b02809ae48523319983dd41fb9f3ab9e53044eb72d44eac57057c518e3

Observation b237f438-8722-4049-abc5-19bbeb767f8f · outbound

This paper cites Grassmannians and Cluster Algebras.

Singularities of massless scattering and cluster algebras Grassmannians and Cluster Algebras

Reference 2003

Resolution
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source=pdf_text observed=2026-08-06T21:09:05.169528Z digest=sha256:47380fba0747d4ff4380c17b2a1a1cd0c892bf6a56eed09f1e1fbc03d7d23eca

Observation 9b1b2793-167f-4b2d-8ef5-30d7602c1a6c · outbound

This paper cites URL http: //dx.doi.org/10.1103/PhysRevLett.126.091603.

Singularities of massless scattering and cluster algebras URL http: //dx.doi.org/10.1103/PhysRevLett.126.091603

Reference 7114

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source=pdf_text observed=2026-08-06T21:09:05.296127Z digest=sha256:0a68a043016fddcf1f11d0f7da935af5e00569f54c16a89c0bad249d146216a5

Observation b3e3089c-4fd6-4ab3-8216-192878438d86 · outbound

This paper cites URL http://dx.

Singularities of massless scattering and cluster algebras URL http://dx

Reference 8479

Resolution
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doi, observed 2026-08-06T21:09:09.822713Z

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source=pdf_text observed=2026-08-06T21:09:05.823872Z digest=sha256:2ab7066c9586e7a44bc73cb4b8c89423bbc71c2c780b0994544ec3a4f3ffb729

Pith citing papers

Observation ea0441d7-55bf-4060-a7b2-144ec2d15684 · inbound

Geometric Landau Analysis and Symbol Bootstrap cites this paper.

Geometric Landau Analysis and Symbol Bootstrap Singularities of massless scattering and cluster algebras

Reference 103

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no resolver link, observed 2026-08-05T23:22:48.010474Z

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source=arxiv_source observed=2026-08-05T23:22:48.010474Z digest=sha256:3c7ca31e1977b01a77e14cd023f6df43df026523ad20ff4f6fa8bd4b5bb4e945

Observation 4db6d7c9-52a0-48b4-bee0-ed1aa944065e · inbound

Novel cluster-algebraic letters for 5- and 6-point QCD processes cites this paper.

Novel cluster-algebraic letters for 5- and 6-point QCD processes Singularities of massless scattering and cluster algebras

Reference 33

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no resolver link, observed 2026-08-02T18:05:13.216113Z

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source=pdf_text observed=2026-08-02T18:05:13.216113Z digest=sha256:fbe3e0fcbc6e4138efa19e2dc6dda3aabf57c9e307ec841bb7a785ebae50e497

Observation fd57f4da-87d6-4ac8-84bb-e266cc0cba35 · inbound

Bootstrapping two-loop six-gluon amplitudes in QCD cites this paper.

Bootstrapping two-loop six-gluon amplitudes in QCD Singularities of massless scattering and cluster algebras

Reference 25

Resolution
verified exact
arxiv_id, observed 2026-07-01T17:05:50.642379Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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